How solid is a dipolar supersolid?

The conceptual roots of supersolidity can be traced back to 1960, when Eugene Gross calculated the appearance of long-range spatial order in the ground state of a system of interacting bosons. In 2004, an abrupt change in the shear modulus of solid Helium-4 was interpreted as the first experimental evidence of a solid-to-supersolid transition. However, this proved to be a false dawn, with the shear modulus shift arising from structural changes in the classical solid instead. The eventual experimental observation materialized via a superfluid-to-supersolid phase transition in ultracold gases, with particular success in dipolar Bose Einstein condensates (BECs) [1]. To complement this robust experimental platform, we use the extended Gross-Pitaevskii equation (eGPE) to theoretically probe the distinctly solid properties of the supersolid. We shear the crystal to produce perpendicular shear waves in the supersolid --- this transverse wave only propagates in solids, and can be probed across the BEC-to-supersolid transition. We find the appearance of a non-zero shear modulus at the BEC-to-supersolid transition, which increases as the superfluid fraction is reduced. Our results match closely with a semi-analytic model for the crystal deformation.

[1] L. Chomaz et al., Rep. Prog. Phys. 86 026401 (2022).